Palindrome question

[jayant.apte]

A palindrome is a number that reads the same forward and backward, such as 121. How many odd, 4-digit numbers are palindromes?
40
45
50
90
2500

I was expecting the answer to be 45. I got this by -

1st and last digits are odd, so 1, 3, 5, 7, 9 - 5 ways
middle 2 digits can range from 0-9, so 10 ways. BUT, palindrome means that the digits in the middle cannot be the same as the outer digits so shouldn't we subtract 1 from 10 way = 9 ways.

And then we get 5 x 9 = 45

OA is 50

Thanks for your help.

[nitin_prakash_khanna]

In my opinion the only mistake you are making is when you are thinking that the middle digit cant repeat. It can.....

the number could be
1111
9999
or similar...

so you have 5 ways for 1st and last digit and 10 ways for the 2nd and 3rd digit...in total 5*10 = 50 numbers

The palindrome reads the same forward and reverse ,question doesnt say that repetition of digits is not allowed.

[RonPurewal]

hi -

BUT, palindrome means that the digits in the middle cannot be the same as the outer digits

where'd you get that idea?

the definition of a palindrome requires only that the number read the same both forward and backward; there is no stipulation that any of the digits be different.

as the poster above has correctly asserted, numbers such as 1111 and 9999 are also palindromes.

so, the first digit can be 1, 3, 5, 7, or 9; the second digit can be anything at all (ten possibilities). therefore, there are 5 * 10 = 50 such palindromes.

[sudipto.impmail]

Why first digit has only five options? Is 2222 is not a palindrome?

[gokul_nair1984]

Why first digit has only five options? Is 2222 is not a palindrome?

Because the first digit will be the same as the last digit(which can have only 5 options viz.1,3,5,7,9 as the number has to be odd)!!!


Furthermore, 2222 is a palindrome but it is not an odd palindrome.
Please read the question carefully!!

[mschwrtz]

Yup, right answers all.

But take a breath gokul_nair1984. Two exclamation points?? sudipto.impmail is entitled to make a mistake, just as we all are (and do).

[mschwrtz]

In fact, now that I think of it, if you search my posts here you'll find at least three mea culpae (about one admitted mistake per hundred posts, mostly careless).

[gokul_nair1984]

I never meant to be obnoxious( and those exclamations just don't mean anything to me). I apologise if that offended anyone.

[mschwrtz]

No worries here Gokul, I'm just being overcautious. On a forum like this one, everything that you know how to do can seem obvious, and every mistake that someone else makes can seem easily avoidable.

Let me tell you a related story: A few instructors wrote math questions and explanation, then sent them to other instructors for editing. The guy who edited my questions happened to be the same Ron who's so prolific here. He pointed out that I used the word "obviously" or some synonym in about half my explanations. Not good. If it were obvious to the reader he wouldn't be looking at an answer key.

[gokul_nair1984]

Got the point. Thank you.

[mschwrtz]

; )